Economic development and the return to human capital: a smooth ...

JOURNAL OF APPLIED ECONOMETRICS J. Appl. Econ. 21: 111– 132 (2006) Published online 9 June 2005 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/jae.813

ECONOMIC DEVELOPMENT AND THE RETURN TO HUMAN CAPITAL: A SMOOTH COEFFICIENT SEMIPARAMETRIC APPROACH THEOFANIS P. MAMUNEAS,a ANDREAS SAVVIDESb AND THANASIS STENGOSc * b

a Department of Economics, University of Cyprus, Cyprus Department of Economics, Oklahoma State University, USA c Department of Economics, University of Guelph, Canada

SUMMARY This paper investigates the impact of human capital on the process of economic growth by allowing the contribution of traditional inputs (capital and labour) as well as that of human capital to vary both across countries and time. The former is accomplished by constructing an index of TFP growth for traditional inputs, while the latter through semiparametric methods. We derive estimates of the output elasticity and social return to human capital for 51 countries at various stages of economic development. Copyright  2005 John Wiley & Sons, Ltd.

1. INTRODUCTION The contribution of human capital to the growth of income is controversial. At the micro level, there is consistent evidence that education raises incomes significantly (commonly referred to as Mincerian wage regressions). Evidence at the macro level has been mixed. Studies such as Barro (1991), Bils and Klenow (2000), Mankiw et al. (1992) and others use enrollment rates and find a positive and significant contribution for human capital to the growth of output (GDP). Benhabib and Spiegel (1994), Kyriacou (1991), Lau et al. (1991) and Pritchett (2001), however, find an insignificant or even negative contribution for the stock of human capital (mean years of schooling). The estimated effect for human capital does not hinge on the way it is defined (as stock or flow).1 For example, Barro and Sala-i-Martin (1995) find the impact of enrollment rates to be insignificant while mean years of schooling has a positive and significant effect on economic growth. Recent work has focused on the possibility of multiple regimes and nonlinearities in the human capital–growth process. Durlauf and Johnson (1995) and Masanjala and Papageorgiou (2002) use the regression-tree and the threshold-regression methodology to show the existence of multiple regimes. Kalaitzidakis et al. (2001) use semiparametric techniques and find that there are substantial nonlinearities in the growth–human capital relationship that linear models are unable to detect. Kourtellos (2003) also uses a semiparametric coefficient model to study a local generalization of the Solow model in the spirit of Durlauf et al. (2001). He examines two possibilities: first, the parameters of the Solow growth model are a smooth unknown function of Ł Correspondence to: Thanasis Stengos, Department of Economics, University of Guelph, Guelph, Ontario, N1G 2W1, Canada. E-mail: [email protected] 1 Early studies tended to use a flow measure (enrollment rates) while more recent studies have used a stock measure (mean years of schooling derived from cumulating past enrollment rates).

Copyright  2005 John Wiley & Sons, Ltd.

Received 22 July 2003 Revised 7 June 2004

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the literacy rate and second, a function of life expectancy (interpreted as a measure of the quality of human capital). The main purpose of this paper is to estimate a general model of the economic growth process by allowing the contribution of both ‘traditional’ inputs (capital and labour) and human capital to vary across both countries and time. In the first place we calculate an index of total factor productivity (TFP) growth that contains only the contribution of the ‘traditional’ inputs (capital and labour). This index uses measured data on the share of labour and capital in total output and thus eschews the estimation of a production function with the implicit assumption that the output contribution of capital and labour is constant. This is an important attribute because all previous studies (including ours) contain countries at widely differing stages of economic development, obviating the need to relax the assumption of a constant contribution both intra- and inter-temporally. Next, we use this index to evaluate the impact of human capital growth on the growth of TFP. We accomplish this via a semiparametric smooth coefficient model that allows for the effect of human capital on economic growth to be nonlinear. Theoretical work by Azariadis and Drazen (1990) has demonstrated that the way in which human capital impacts the growth of output differs across countries. In particular, threshold externalities may exist as a result of attaining a ‘critical mass’ in human capital and, therefore, economies that are similar in terms of technology or preferences may display substantial differences in growth rates if they lie on either side of the threshold. In Durlauf (1993), local technological spillovers generate multiple growth equilibria characterized by differences in the way in which the traditional inputs are employed in aggregate production. An important contribution of our work is the construction of estimates of the elasticity of output with respect to human capital that display a rather large variation across countries, casting doubt on the equality assumption in the literature. Moreover, for a number of the developing economies in our sample, human capital (mean years of schooling) has no significant effect on aggregate output, a possibility mentioned in the literature (e.g. Pritchett, 2001) but not explored in a systematic fashion empirically. In the next section we present our methodology. We construct a traditional index of TFP growth that does not rely on the estimation of a production function with the concomitant assumption of constant capital and labour contributions across countries and time. In the third section we present the smooth coefficient semiparametric model that allows the effect of human capital on TFP growth to be nonlinear. This methodology enables us to derive country (and time)-specific estimates of output elasticities and social rates of return for human capital. The final section concludes the paper.

2. METHODOLOGY The treatment of human capital in cross-country (macro) studies falls into three main categories: (a) a production function is combined with equations for the accumulation of reproducible factors to arrive at equations for the steady state of per capita income and the transition process to the steady state (e.g. Mankiw et al., 1992 and the substantial literature spawned by this study); (b) a production function that includes human capital as either an input or as a determinant of total factor productivity is estimated directly (e.g. Benhabib and Spiegel, 1994; Edwards, 1998; Pritchett, 2001); and (c) specific values are assigned to the coefficients of the production function (the shares of inputs) to arrive at an estimate of the residual which is then evaluated, along with the factors of production (including human capital), for their contribution to differences in the level or Copyright  2005 John Wiley & Sons, Ltd.

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growth of per capita GDP (e.g. Hall and Jones, 1999; Klenow and Rodr´ıguez-Clare, 1997). Most of these studies are based on very restrictive assumptions: a Cobb–Douglas production function with Hicks-neutral technology. By contrast, our study relies on a general framework. We assume that a general production function describes the technology of country i at time t as follows: Y D fK, E, H, t

1

where Y, K and E represent the amounts of total output, physical capital and effective or humancapital augmented labour, respectively, H is average human capital (mean years of schooling per person of working age) and t is a technology index measured by the time trend. Total differentiation of (1) with respect to time and division by Y yields C εK K DA C εE E C εH H Y

2

D ∂f/∂t/Y is the exogenous rate of technological change where denotes a growth rate, A and εQ D ∂ ln Y/∂ ln Q Q D K, E, H denotes output elasticity. The last term in (2) measures the externality effect on human capital accumulation. This effect is emphasized by recent endogenous growth models initiated by Lucas (1988). Assuming a perfectly competitive theory of distribution, the output elasticities of effective labour and capital should be equal to the observed income shares of labour, sYL and capital, sYK .2 Equation (2), however, is not useful for empirical purposes is not observable. because the growth rate of effective labour E Assuming that the effective labour input is a function of the labour force and average human capital, or E D gL, H 3 as we can decompose E

D L L C H H E

4

where L and H are effective labour elasticities with respect to labour and average human capital, respectively. Substituting (4) in (2) we have: C εK K DA C εE L L C εE H C εH H Y

5

By contrast with (2), the last term in parentheses in (5) measures the total effect of human capital, while the output elasticity of raw labour is εE L . Direct estimation of (5) corresponds to the well-known growth accounting methodology. As mentioned previously and by several authors (e.g. Temple, 1999), an important criticism of estimating a model such as (5) is the assumption that the contribution of inputs is the same across countries and time so the estimated parameters represent an ‘average’ contribution. In the remainder of the paper we address this issue through an alternative specification that accounts for differing contributions of all productive inputs. In the first instance, we construct an index of TFP growth for our panel that contains only the traditional inputs. This index allows the contribution 2 The income share of labour can be defined in two ways: the income share of effective labour (E) or the income share of ‘traditional’ or workforce labour (L). These two are equal since the value of labour (the numerator of the income share) is the same independently of the definition of the labour input as L or E (the corresponding price and quantity indices, however, will differ).


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of capital and labour to differ both intra- and inter-temporally and to be dictated by the data. We define a T¨ornqvist index of TFP growth for country i 1, . . . , N in year t 1, . . . , T as follows: it D Y it sEit L it sKit K it TFP

6

where sEit D 0.5SLit C SLit1 and sKit D 0.5SKit C SKit1 are weighted averages of the cost it D ln Qit shares of labour and physical capital (SLit and SKit , defined in Appendix A) and Q 3 ln Qit1 Q D Y, L, K. This measure of TFP contains the component of output growth that cannot be explained by the growth of ‘traditional’ inputs (K and L). This index will be an exact index of exogenous technological change under certain conditions (see Diewert, 1976) and as long as the production function contains only the traditional inputs. The production function underlying this index is a general translog. It should be stressed, however, that if human capital enters the production function as in (1), this index is a biased index of technological change and, therefore, will affect TFP growth as defined in (6). In what follows we present a methodology variations in H for estimating this effect. Subscripting equation (5) by country and year (it), taking a discrete approximation of the continuous growth rates and adding (6) to it we have: it C [εKit sKit K it D A it C εEit L sEit L it ] TFP it C εEit Hit C εHit H

7

it is the exogenous rate of technological change, and the final term in where the first term A parentheses is the total contribution of human capital. The latter is made up of two components: the first is the direct or private effect of human capital and the second is the indirect or externality effect. The term in brackets is the scale effect. Under constant returns to scale, output elasticities will be equal to the cost shares and the term in brackets will be equal to zero if L D 1.4 It can be shown that the first-order conditions of standard cost minimization with respect to physical capital and labour (taking average human capital as given) imply that

εjit D sjit ,

j D K, E

8

where D ε1 CY is the elasticity of returns to scale of capital and labour and εCY D ∂C/∂Y/Y/C is cost flexibility. Of central importance to our study is the final term in (7) that captures the contribution of it . human capital to aggregate production. We model this as a general unknown function ÐH Details on the specification and estimation of the Ð function will be provided in the following section. Using the above formulation for Ð and (8), (7) can be written as it C ˛M it D A it C ÐH it TFP

9

3 The cost shares of effective and ‘traditional’ labour are the same independently of how we define labour because labour cost should be the same. Thus sEit sLit , where E and L denote, as before, an index of effective and ‘traditional’ labour input. 4 The condition D 1 will be true if (3) is linear homogeneous in L or the production function for effective labour L can be written as gL, H D LϕH, where ϕH is any function of H. Many popular models belong to this class of effective labour production function. For example, Lucas (1988) postulates that gL, H D LH. Another possibility is a Mincerian-type production function gL, H D Le H assumed by Hall and Jones (1999).


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it D sK K it C sEit L it . Estimation of (9) allows testing the hypothesis of where ˛ D 1 and M it nonconstant returns to scale in capital and labour ˛ 6D 0. Moreover, it allows human capital to influence TFP growth in a nonlinear fashion. In the following section the nonlinear aspects of human capital growth are investigated systematically via semiparametric estimation. Equation (9) forms the basis of our empirical analysis. It is important to note that the form and interpretation of (9) depends on the definition of the TFP growth index in (6). Our objective is to identify the total effect of human capital (direct plus indirect) under minimal assumptions. Therefore in (6) we define an index that can be constructed from observable data and can yield estimates of the total effect. For instance, instead of (6) we can define a TFP growth index by subtracting from output growth the (cost-share) weighted growth it D Y it sEit E it sK K it , or by subtracting rates of effective labour and physical capital, TFP it from output growth the (cost-share) weighted growth rates of labour and capital where the labour it D Y it sb L weight is based on the cost share of unskilled or raw labour sLb it , TFP Lit it sKit Kit . These alternative definitions of the TFP index will not meet our objectives. Using these alternative indices would require information on effective labour or the raw labour cost share, neither of which is directly observable. It could be argued, however, that these can be obtained by making assumptions about the private contribution of human capital or by using estimates from micro studies. Clearly, if these assumptions or estimates are not correct they may bias the total effect of human capital. In summary, defining a TFP growth index as in (6) that is based on observable data appears to us appropriate.

3. ESTIMATION AND EMPIRICAL RESULTS 3.1. Estimation Method it (exogenous growth of technological change) In order to estimate equation (9) we model A as a function of country- and year-specific dummy variables. Country-specific dummies Di capture idiosyncratic exogenous technological change and time-specific dummies Dt capture the procyclical behaviour of TFP growth. In alternative specifications we include political and economic freedom and a country’s trade orientation as additional determinants of TFP growth. The rationale for this is that increased exposure to international trade promotes technology absorption and boosts productivity. Edwards (1998) provides evidence linking outward orientation Z1 with TFP growth. The role of institution building as a determinant of long-run economic performance has received considerable attention recently. Rodrik (2000) discusses five types of institutions: property rights, regulatory institutions, institutions for macroeconomic stabilization, institutions for social insurance and institutions of conflict management. He argues that building institutions can be thought of as a form of technology transfer that allows increased productivity. Participatory democracy is a meta-institution that helps build better institutions. He provides evidence that participatory democracy improves economic performance both in terms of higher long-run growth rates and short-term stability. We include two measures of participatory democracy: an index of political freedoms Z2 and civil freedoms Z3 .5 As for the unknown function Ð, we estimate two alternative specifications: (i) it depends only on the level of human capital and (ii) in addition to the level of human capital it also depends 5 Details on the measurement of the political and civil freedom indexes and outward orientation are provided in Appendix A.


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on other economy characteristics . In our case will be Z1 , the outward orientation variable. Appending an error term, uit , equation (9) then becomes it D a0 C TFP

N1

ai Di C

iD1

T1

at Dt C

tD1

3

it C H it Hit , it C uit bs Zsit C ˛M

sD2

it Hit , it C uit D Xit ˇ C H

10

it and the error term satisfies Euit jXit , Hit , H it , it D 0. where Xit D Di , Dt , Zsit , M The central issue in (10) is the estimation of the Ð function. The estimation approach adopted here is based on the smooth coefficient semiparametric model (see Fan, 1992; Fan and Zhang, 1999; Cai et al., 2000a,b; Li et al., 2002; Kourtellos, 2003). It is a generalization of varying coefficient models and follows the local polynomial linear regression of Stone (1977) and Fan (1992), as well as the widely used Nadaraya–Watson constant kernels. The general description of the method follows. The data are given as fYi , Wi g, i D 1, . . . , n, a realization from an i.i.d. random vector fY, Wg, where for notational simplicity we suppress the observation subscript it as i D 1, . . . , n, with n D N ð T. The covariates are defined on W